Finite Group Databasebeta

← #27193483

Subgroups — #27193483

Order 13184.

300 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic
2#20267845C212yesmaximal, complemented
3#20267515C211yesmaximal, characteristic, complemented
4#20267514C212yesmaximal, complemented
5#323×C103C211yesmaximal, characteristic, complemented
6C22×C22⋊D103C411yescharacteristic
7C23×Dic103C411yescharacteristic
8C22×C4×D103C411yescharacteristic
9(C22⋊D103)⋊C4—22no—
10(C22⋊D103)⋊C4—22no—
11C2×Dic103⋊C4C411yescharacteristic
12C2×(C2×D103)⋊C4C2211yescharacteristic
13C2×C4×Dic103C2211yescharacteristic
14Dic103⋊C8—22no—
15C22⋊(C103⋊C8)C2212yes—
16#15692931—22no—
17C2×C22⋊C4×C103C2211yescharacteristic
18C22⋊C8×C103C2212yes—
19C23×D103C2×C411yescharacteristic
20C2×C22⋊D103—22no—
21C2×C22⋊D103—22no—
22C2×C22⋊D103—22no—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C22×Dic103—42no—
26C22×Dic103C2×C411yescharacteristic
27C22×Dic103C2×C411yescharacteristic
28C22×Dic103C2×C411yescharacteristic
29C2×C4×D103—21no—
30C2×C4×D103—21no—
31C2×C4×D103—42no—
32C2×C103⋊C8—22no—
33Dic103⋊C4—22no—
34(C2×D103)⋊C4—22no—
35C4×Dic103D412yes—
36C4×Dic103D412yes—
37C24×C103C2×C411yescharacteristic
38C22×C4×C103C2×C411yescharacteristic
39C22×C4×C103C2311yescharacteristic
40C2×C8×C103—22no—
41C22⋊C4×C103—22no—
42C23×C103—21no—
43C23×C103—21no—
44C23×C103—41no—
45C23×C103—41no—
46C23×C103M1612yes—
47C23×C103C22×C411yescharacteristic
48C22×D103—21no—
49C22×D103—21no—
50C22×D103—41no—
51C22×D103—41no—
52C22×D103M1612yes—
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103C2×D412yes—
57C22⋊D103—28no—
58C2×Dic103—21no—
59C2×Dic103—21no—
60C2×Dic103—22no—
61C2×Dic103—21no—
62C2×Dic103—42no—
63C2×Dic103—42no—
64C2×Dic103—41no—
65C2×Dic103C22⋊C412yes—
66C2×Dic103C22⋊C411yescharacteristic
67C2×Dic103C22⋊C411yescharacteristic
68C4×D103—42no—
69C4×D103—42no—
70C8×C103—42no—
71C103⋊C8—42no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103—22no—
75C22×C103—42no—
76C22×C103—42no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103C2×C22⋊C411yescharacteristic
80C22×C103C2×M1611yescharacteristic
81C22×C103C2×M1611yescharacteristic
82C2×D103—22no—
83C2×D103—42no—
84C2×D103—41no—
85C2×D103—41no—
86C2×D103—42no—
87C4×C103—22no—
88C4×C103—41no—
89Dic103—22no—
90Dic103—21no—
91Dic103—41no—
92Dic103#10012yes—
93C2×C103—21no—
94C2×C103—21no—
95C2×C103—42no—
96C2×C103#40711yescharacteristic
97C2×C103#41011yescharacteristic
98C2×C103C2×#10011yescharacteristic
99D103—42no—
100#1466—1031nomaximal, Sylow
101C103#146611yescharacteristic, complemented, Sylow
102C2×C4×D4—1031no—
103#432—1032no—
104#323—1031no—
105#323—1032no—
106#323D10311yescharacteristic, complemented
107C22×D4—1031no—
108C23×C4—1031no—
109C23×C4—1031no—
110C4×D4—2062no—
111C4×D4—2062no—
112C2×C4⋊C4—1031no—
113C2×C22⋊C4—1031no—
114C2×C22⋊C4C2×D10311yescharacteristic
115C2×C42—1031no—
116C4⋊C8—2062no—
117C22⋊C8—1032no—
118C22⋊C8C2×D10312yes—
119#97—2062no—
120C24—1031no—
121C24C4×D10311yescharacteristic
122C2×D4—2062no—
123C2×D4—2062no—
124C2×D4—2062no—
125C22×C4—1031no—
126C22×C4—1031no—
127C22×C4—1031no—
128C22×C4—4122no—
129C22×C4—4122no—
130C22×C4—2061no—
131C22×C4—2061no—
132C22×C4—2061no—
133C22×C4—2061no—
134C22×C4C4×D10311yescharacteristic
135C22×C4C22×D10311yescharacteristic
136C2×C8—22no—
137C2×C8—2062no—
138C4⋊C4—2062no—
139C22⋊C4—22no—
140C22⋊C4—2062no—
141C42—1032no—
142C42—1032no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—1032no—
148C23—4121no—
149C23—4121no—
150C23—2061no—
151C23—2061no—
152C23#1311008812yes—
153C23C2×C4×D10311yescharacteristic
154D4—2068no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—1031no—
159C2×C4—1032no—
160C2×C4—1031no—
161C2×C4—4122no—
162C2×C4—4122no—
163C2×C4—4122no—
164C2×C4—4122no—
165C2×C4—4121no—
166C2×C4—2062no—
167C2×C4—2061no—
168C2×C4—2061no—
169C2×C4—2061no—
170C2×C4D4×D10312yes—
171C8—42no—
172C8—4122no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—4122no—
181C22—4122no—
182C22—4121no—
183C22—4121no—
184C22—2062no—
185C22C22⋊C4×D10311yescharacteristic
186C22M16×D10311yescharacteristic
187C22C2×#1311008811yescharacteristic
188C4—22no—
189C4—41no—
190C4—1032no—
191C4—4121no—
192C4—2062no—
193C4—2061no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—4122no—
198C2#2026775311yescharacteristic
199C2#2026776311yescharacteristic
200C2#100×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#323×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC22×C22⋊D103C4
cosocleC22×C4×C103C23
hypercenter#323D103
hypocenterC103#1466
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20267845C2semidirect
3. #20267515C2semidirect
4. #20267514C2semidirect
5. #323×C103C2semidirect
101. C103#1466semidirect
106. #323D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×(C22⋊D103)⋊C42
#202678452
#202675152
#202675142
#323×C1032
#1466103